The shortage function has recently been introduced in portfolio selection theory for measuring efficiency. In this paper we focuss on the case of shortselling. We show that, in such a case, the shortage function can be computed in closed form. Some issues concerning duality are also analyzed. We...

Luenberger [8] introduced the so-called benefit function that converts preferences into a numerical function that has some cardinal meaning. This measure has a number of remarkable properties and is a powerful tool in analyzing welfare issues ([10], [12], [13], [14]). This paper studies the...

This paper extends the recent work by Frei and Harker on projections onto efficient frontiers (1999) in three ways. First, we provide a formal definition of the production set as the intersection of a finite number of closed halfspaces. We emphasize the necessity of a complete enumeration of the...

This contribution compares existing and newly developed techniques for geometrically representing mean–variance–skewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage...

This paper proposes a pragmatic, discrete time indicator to gauge the performance of port-folios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of...

The main aim of this contribution is to compare existing and newly developed techniques for geometrically representing mean-variance-skewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based...

This note shows how the linear programs needed to compute cost and revenue functions under constant returns to scale and a single output or input, respectively, can be replaced with a more efficient enumeration algorithm. An empirical illustration shows the gain in computer time one can obtain.